{"id":"https://openalex.org/W2116333964","doi":"https://doi.org/10.1155/2012/563586","title":"Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems","display_name":"Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2116333964","doi":"https://doi.org/10.1155/2012/563586","mag":"2116333964"},"language":"en","primary_location":{"id":"doi:10.1155/2012/563586","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/563586","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/563586.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/563586.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101515549","display_name":"Guangbin Wang","orcid":"https://orcid.org/0000-0002-1531-3275"},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guangbin Wang","raw_affiliation_strings":["Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061","institution_ids":["https://openalex.org/I143413998"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021346034","display_name":"Yanli Du","orcid":null},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanli Du","raw_affiliation_strings":["Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061","institution_ids":["https://openalex.org/I143413998"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022906126","display_name":"Fuping Tan","orcid":"https://orcid.org/0000-0001-7985-732X"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fuping Tan","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 200444"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 200444","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101515549"],"corresponding_institution_ids":["https://openalex.org/I143413998"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3456,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.64497143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7768200635910034},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6275389194488525},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.559359610080719},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.45611023902893066},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3669310510158539},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32983386516571045},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14688169956207275},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.04305204749107361}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7768200635910034},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6275389194488525},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.559359610080719},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.45611023902893066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3669310510158539},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32983386516571045},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14688169956207275},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.04305204749107361},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/563586","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/563586","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/563586.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1357153505","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1357153505","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:563586","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/563586.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:c1e11dc8b03b49da8dd65e0b787e5ad9","is_oa":true,"landing_page_url":"https://doaj.org/article/c1e11dc8b03b49da8dd65e0b787e5ad9","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/563586","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/563586","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/563586.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3188788837","display_name":null,"funder_award_id":"11001144","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6718186334","display_name":null,"funder_award_id":"J10LA06","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2116333964.pdf","grobid_xml":"https://content.openalex.org/works/W2116333964.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W2009379438","https://openalex.org/W2026655828","https://openalex.org/W2035830474","https://openalex.org/W2060343497","https://openalex.org/W2141944350","https://openalex.org/W3035235874","https://openalex.org/W4295016751"],"related_works":["https://openalex.org/W79007405","https://openalex.org/W330473954","https://openalex.org/W2368062247","https://openalex.org/W4319880936","https://openalex.org/W2146954624","https://openalex.org/W4236547055","https://openalex.org/W1965270833","https://openalex.org/W1997267293","https://openalex.org/W2044779088","https://openalex.org/W3093603618"],"abstract_inverted_index":{"We":[0,14],"present":[1],"preconditioned":[2,25,36],"generalized":[3],"accelerated":[4],"overrelaxation":[5],"methods":[6,38],"for":[7],"solving":[8],"weighted":[9],"linear":[10],"least":[11],"square":[12],"problems.":[13],"compare":[15],"the":[16,20,24,27,35,42,46],"spectral":[17],"radii":[18],"of":[19,23],"iteration":[21],"matrices":[22],"and":[26],"original":[28],"methods.":[29],"The":[30],"comparison":[31],"results":[32],"show":[33],"that":[34],"GAOR":[37,43,47],"converge":[39],"faster":[40],"than":[41],"method":[44,48],"whenever":[45],"is":[49],"convergent.":[50],"Finally,":[51],"we":[52],"give":[53],"a":[54],"numerical":[55],"example":[56],"to":[57],"confirm":[58],"our":[59],"theoretical":[60],"results.":[61]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}